Police were called at about 11.15pm on Sunday, January 2.
The altercation took place close to a white van and a silver Audi, which were then both driven off.
Three men have been arrested in connection with the incident and remain in police custody.
An investigation into the circumstances has been launched and we are appealing to any witnesses to come forward.
A spokesman from Derbyshire Police said: “We particularly want to hear from anyone who saw the two vehicles being driven along the A6 around the time or afterwards – and drivers with dashcam devices who were in the area are also urged to get in touch."
Anyone with information should contact the police by calling 101 quoting reference 22*3458, send a private message to /DerbyshireConstabulary on Facebook or direct message the contact centre on @DerPolContact on Twitter.